Considered here is the well-posedness of a KdV-type Boussinesq system modeling two-way propagation of small-amplitude long waves on the surface of an ideal fluid when the motion is sensibly two dimensional. Solutions are obtained in a range of Sobolev-type spaces, from the energy level to the analytic Gevrey spaces. In addition, a criterion for detecting the possibility of blow-up in finite tim...

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification int...

2014 We present here a generalization of the Boussinesq approximation of interest in the thermohydrodynamic study of a horizontal fluid layer heated from below (Rayleigh-Bénard problem) when the depth of the layer is important. A straightforward dimensional analysis of the problem shows under which conditions one cannot neglect, however small, the isothermal compressibility. We discuss also the...

A simple model to explain the numerically observed behavior of chaotically varying stripes and square patterns in zero-Prandtl-number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher-order modes, may lead to a competition between the two sets of rolls. The appearance of square patterns is due to a secondary forward b...

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect t...

this paper modeled heating air of a room through examining free convection in a 3d chamber. the chamber had cold and hot sources with tc and th temperatures, respectively. its other walls were adiabatic. this study aimed at predicting effect of temperature difference, displacement of hot and cold sources and their aspect ratio on flow field, temperature and heat transfer rate. to conduct the st...

We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flow of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric ...

As shown in earlier work [Ahlers, J. Fluid Mech. 569, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient. If the working fluid is ethane close to the critical point, the origin of non-Ober...

We investigate here the interactions of waves governed by a Boussinesq system with partially immersed body allowed to move freely in vertical direction. show that whole equations can be reduced transmission problem for conditions given terms displacement object and average horizontal discharge beneath it; these two quantities are turn determined nonlinear ODEs forcing coming from exterior wave-...

We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the N -dimensional ...